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I know that there are (at least) three types of personal pronouns in Spanish (well, and English): direct, indirect, and reflexive. In cases where all three (or at least two) are present, what is the correct ordering of these pronouns?

Also, why is this the correct ordering of these pronouns? That is, is there a reason that the order is...whatever it is?

Also remember the la-la rule: if both pronouns start with the letter l, change the first pronoun to se.

As to why it is how it is, I wasn't able to find anything. This is most likely part of the natural evolution of a language over time, as opposed to an instance of grammarians sitting down and deciding on a rule.

It is very possible to use three pronouns in sequence: la vida te me la llevaste and the order is not always as indicated here. The "rule" given works 95+% of the time, but doesn't handle all situations. Consider swapping the first and second persons in the triple object example: la vida te me la llevé is the correct form, but it's IRD, not RID.
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guifaJul 23 '14 at 4:18

The accepted answer isn't right. If you have te and me as two different objects, they will always go in the same order. You can only have te me, and never me te, likewise, you can never have le me, even if le is the indirect object and me is the direct object.

Consider, for example, "te me acercas". te is the reflexive object, and me is the indirect. Now switch it from meaning "you are approaching me" to "I am approaching you". If you follow RID, you get "me te acerco" which is absolutely wrong. It should be te me acerco although because that sounds rather rebuscado, you will normally just see me acerco a ti, and as a result I've only really seen it in poetry or similarly exalted language:

When direct objects and indirect objects appear together, the direct object is usually one of the following four pronouns: lo, la, los or las. The me, te and nos forms rarely show up as direct pronouns in the same construction with indirect pronouns. Similarly, in English one might say “He gave it to us” but one would rarely use a phrase like “He gave us to it.” (even though grammatically correct).

When the indirect pronouns le or les are followed by the direct object lo, la, los, las appears in the same construction, le/les must be converted to se. Thus a phrase le doy el libro (I gave him the book), would become se lo doy (I gave him it) not le lo doy.

The result of the previous two rules put together means that in 95% of cases where direct and indirect objects are used in the same construction, it will take the form of one of me/te/se/nos followed by one of lo/la/los/las:

Se la pasé a él. I handed it to him.Nos lo llevó ayer. He took it for us yesterday.
Juan me lo dio. Juan gave it to me.

2. Reflexive-Direct

In this pattern, the reflexive pronoun essentially takes on the role of an indirect pronoun, and follows the same rules: The reflexive (indirect) precedes the direct, and the direct form is nearly always one of lo/la/los/las.

I put it on. Me lo pongo.
This overcoat, will you take it? Este abrigo, ¿te lo llevas?

This construction presents a pattern that is almost non-existent in English. In English we would say: "I broke the cup", but in Spanish one would say Se me rompió la taza. "The cup broke itself to (for, on) me." The cup, which is the noun object in English, becomes the subject in Spanish (and governs the agreement of the verb). The verb appears in Spanish with a reflexive pronoun, which is always se, since only things--therefore 3rd person--can appear as subjects).

There are a relatively small handful of common reflexives that use this pattern:

In summary, the Reflexive-Indirect pattern will virtually always consist of se followed by an indirect pronoun.

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Rules of thumb like RID comes in handy if you are trying to work out an uncommon case for a test, but will hinder fluency if you rely on it for real-time speech. If your goal is to be able to speak comfortably, you are better off focusing on learning the relatively small of common patterns so that you can quickly recognize and reproduce them.